They are about two inches wide, squarish, and five inches tall. They hail from the Toggenburg valley of northeast Switzerland, and they are held in the highest regard by experts around the world.

They are glass bottles used to hold athletes’ urine samples, and they are central to the account of a former Russian antidoping official who says that the host country executed an elaborate doping operation at the 2014 Sochi Olympics — imperceptibly switching out drug-tainted urine from the squat containers long thought to be tamper-proof.

“I tried to break into these bottles years ago and couldn’t do it,” Don Catlin, the former head of the U.C.L.A. Olympic Analytical Laboratory, said. “It’s shocking.”

The bottles, used for testing at the Olympics since the Sydney Games in 2000, are made by Berlinger, a Swiss company founded in 1865 as a mechanical cotton weaving mill. Until this week, they were largely ignored vessels in the global fight against doping.

Now they are prominent characters in an extraordinary ploy that affected the results of the Winter Olympics, according to Grigory Rodchenkov, who ran Russia’s antidoping laboratory for a decade. His accounts of the doping operation were first reported by The New York Times this week.

Berlinger’s bottles were first presented to the International Olympic Committee’s medical commission in the late 1990s, in a meeting in Lausanne, Switzerland, said Andrea Berlinger, the sixth generation of her family to run the company.

Dr. Catlin, then a member of that commission, recalled that the Berlingers showcased various bottle designs to a roomful of doctors. “All of us were particularly pleased and excited by this bottle,” he said, “because it looked pretty bulletproof.”

According to Dr. Rodchenkov, it is not.

Russian officials somehow figured out a way to remove the cap without breaking it, he said, enabling him to replace the steroid-tainted urine of top athletes with clean urine, stockpiled in soda bottles and other containers in the months leading up to the Games.

“We’re all a bit speechless, to be honest,” Ms. Berlinger said Friday. “We’re seeing a lot of support. No one can believe it.”

The mechanics of how the feat was pulled off are a mystery to Dr. Rodchenkov. “I truly believed this was tamper-proof,” he said in a recent interview in Los Angeles, holding a clear Berlinger bottle with a blue stripe in his hand. “This is like a safe. I cannot think how to get under this.”

Russian officials have emphatically disputed Dr. Rodchenkov’s accounts of a state-run doping program. “These allegations look absolutely groundless,” Dmitry S. Peskov, the spokesman for President Vladimir V. Putin, told Russian news agencies in a conference call. “They are not substantiated by any trustworthy data, they are not backed by any sort of documents. All this simply looks like slander by a turncoat.”

Berlinger bottles come in sets of two: one for the athlete’s “A” sample, which is tested at the Games, and the other for the “B” sample, which is used to corroborate a positive test of the A sample. Metal teeth in the B bottle’s cap lock in place, so it cannot be twisted off.

“The bottles are either destroyed or retain visible traces of tampering if any unauthorized attempt is made to open them,” Berlinger’s website says about the security of the bottles.

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A sign for doping control at the 2014 Sochi Games.CreditLee Jin-man/Associated Press

The only way to open the bottle, according to Berlinger, is to use a special machine sold by the company for about $2,000; it cracks the bottle’s cap in half, making it apparent that the sample has been touched.

Dr. Rodchenkov said that for at least 15 Russian athletes who won medals at Sochi, both the A and B samples were substituted before they were tested. None of the bottles’ caps — which are branded with unique seven-digit codes — showed any signs of having been opened.

Each night at Sochi, Dr. Rodchenkov said, sealed bottles were passed through a hole in the wall of the storage closet that served as his shadow laboratory. The bottles were handed to a man who he believed worked for the Russian intelligence service, the F.S.B. Within two hours, he said, those same bottles were returned to him, their caps unlocked.

“Magicians were on duty,” Dr. Rodchenkov said, suspecting that F.S.B. officers had studied the toothed metal rings that lock the bottle when the cap is twisted shut. According to him, they collected hundreds of them leading up to the Olympics.

Dr. Catlin theorized that heat had been applied to remove the bottles’ caps.

He said he had expressed some concern about the bottles years ago, asking if they could be outfitted with internal thermometers, to show if the sample had been frozen or heated. “But that’s just a wild guess,” he said.

After his account was published, Dr. Rodchenkov sent a letter to the World Anti-Doping Agency and the I.O.C., calling on them to examine the B samples of Russian athletes from the 2014 Sochi Games, whom he offered to help identify. Bryan Fogel, an American filmmaker who helped Dr. Rodchenkov flee to Los Angeles, where he now lives, also signed the letter.

While those samples would not contain traces of steroids, Dr. Rodchenkov told The Times, they would bear evidence of tampering. He said there would be scratch marks around the necks of the bottles, where the metal rings are.

He also said that common table salt could be found in some of the samples. When he replaced tainted urine with clean urine, he added salt or water to the new urine to match the chemical specifications of the original sample.

Ms. Berlinger said the bottles were the international standard at major sporting competitions, including the World Cup. Each bottle costs about $15, she said. More than 2,000 athletes competed in the Sochi Games.

Olympics officials have long believed the cost of the bottles to be a critical expense to ensure the integrity of the Games, Dr. Catlin said.

I.O.C. officials have called Dr. Rodchenkov’s account “very detailed and very worrying,” calling on antidoping authorities to investigate his claims.

Asked on Friday for its reaction to Dr. Rodchenkov’s proposal to re-examine the B samples of Russian athletes, a spokeswoman for WADA confirmed receipt of Dr. Rodchenkov’s letter. “We are currently determining our path forward, which we will be in a better position to communicate next week,” she wrote by email.

In the letter, Dr. Rodchenkov and Mr. Fogel asked to be present during any examination of the B samples in Lausanne, requesting that the investigation be carried out by a committee of scientists and an independent observer.

“This could cause all kinds of problems,” Dr. Catlin said. “WADA has got to get on this.”

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Mystery in Sochi Doping Case Lies With Tamper-Proof Bottle. Order Reprints | Today’s Paper | Subscribe